"The world is our laboratory"

A Profile of Myron S. Scholes

[This profile was written for Quantitative Finance, where
a slightly different version appeared in vol. 3, no. 2 (April 2003),
pp. C20--C21. Jacob Bettany, my editor at QF, had the nice idea
of using the quote from Prof. Scholes for the title. --- CRS]

It is no exaggeration to say that one of the main reasons a journal
like Quantitative Finance exists is the work of Myron Scholes.

The story of the Black-Scholes-Merton model is well-known. Scholes became
interested in the problem of derivatives while a Ph.D. student at the
University of Chicago. There he had absorbed the main doctrines of Chicago
School economics, with its emphasis on rational expectations, efficient
markets, the drive towards the efficient frontier, and the utter absence of
free lunches. Already fascinated by the problem of pricing, his interest in
options was awakened around 1967 by a seminar from a fellow student working on
convertible bonds. Shortly afterwards he got his first faculty job at MIT,
where he supervised a large number of master's theses, in one of which a
student tried to explain data on over-the-counter option pricing using the
capital asset pricing model, with less than satisfactory results. There also
he made contact with Fisher Black, who was already interested in options, and
later with Robert Merton, who brought expertise in continuous-time stochastic
processes to the problem of devising hedging strategies.

The central motivation for Scholes was the economic question of
studying the efficiency frontier of portfolios --- how to construct baskets of
assets with optimal trade-offs between risk and return, and in particular what
happened in the limit of riskless portfolios. Surely there was no free
lunch here, no large bills lying on the sidewalk to be picked up by
arbitrageurs, but what did that imply?

The solution, in hindsight, is wonderfully simple. The proper price to put
on an option should equal the expected value of exercising the option. If you
have the option, right now, to sell one share of a stock for $10, and the
current price is $8, the option is worth exactly $2, and the option price
tracks the current stock price one-for-one. If you knew for certain that the
share price would be $8 a year from now, the present value of the option would
be $2, discounted by the cost of holding money, risklessly, for a year --- say
$1. Every $2 change in the stock price a year hence changes the option price
now by $1. If you knew the probability of different share prices in the
future, you could calculate the expected present value of the option, assuming
you were indifferent to risk, which few of us are. Here is the crucial trick:
a portfolio of one share and two such options is actually risk-free, and so,
assuming no arbitrage, must earn the same return as any other riskless asset.
Since we're assuming you already know the probability distribution of the
future stock price, you know its risk and returns, and so have everything you
need to know to calculate the present value of the option! Of course, the
longer the time horizon, the more we discount the future value of exercising
the option, and so the more options we need to balance the risk out of our
portfolio. This fact suffices to give the Black-Scholes formula, provided one
is willing to assume that stock price changes will follow a random walk with
some fixed variance, an assumption which "did not seem onerous" to him at the
time, but would now be more inclined to qualify.

The formula, presented in the now-famous paper "The Pricing of Options and
Corporate Liabilities", had the good fortune to appear shortly after the
opening of the first major market for options, in Chicago, where traders
rapidly adopted it. It also had the good fortune to go on to become one of the
most-cited papers in economics, spawning a whole literature of applications,
modifications and refinements. Ironically, when asked to name
his least appreciated work, Scholes names a companion paper, also with
Black, where they applied the model to empirical data on option prices. (Owing
to a quirk of publishing, it actually appeared before the theoretical paper,
which may have lessened its impact.)

Starting from an economic issue and looking for a parsimonious models,
rather than building mathematical tools and looking for a problem to solve with
them, has been a hall-mark of Scholes's career. "The world is our laboratory",
he says, and the key thing is that it confirm a model's predictive power.
There is a delicate trade-off between realism and simplicity; "tact" is needed
to know what is a first-order effect and what is a second-order correction,
though that is ultimately an empirical point.

The evaluation of such empirical points has itself become a delicate issue,
he says, especially since the rise of computerized data-mining. While by no
means objecting to computer-intensive data analysis --- he has been hooked on
programming since encountering it in his first year of graduate school --- it
raises very subtle problems of selection bias. The world may be our
laboratory, but it is an "evolutionary" rather than an "experimental" lab; "we
have only one run of history", and it is all too easy to devise models which
have no real predictive power. In this connection, he tells the story
of a time he acted as a statistical consultant for a law firm. An expert for
the other side presented a convincing-looking regression analysis to back up
their claims; Scholes, however, noticed that the print-out said "run 89", and
an examination of the other 88 runs quickly undermined the credibility of the
favorable regression. Computerization makes it cheap to do more runs, to
create more models and evaluate them, but it "burns degrees of freedom". The
former cost and tedium of evaluating models actually imposed a useful
discipline, since it encouraged the construction of careful,
theoretically-grounded, models, and discouraged hunting for something which
gave results you liked --- it actually enhanced the meaning and predictive
power of the models people did use!

Surveying the current scene in finance, especially the great diversification
of instruments and the securitization of an immense range of commodities (e.g.,
energy, bandwidth, even carbon emissions), he remains convinced that the
underlying problems of finance and financial theory remain the same.
Reflecting the views of the Chicago school, he says that the goal of financial
markets is to perform society's task of resource allocation; capital markets,
in particular, must "marry" the people who have money to the people who can use
it. The goal of finance is to evolve ways to make this work as smoothly as
possible --- to match the desires of borrowers and lenders, while reducing the
information they need to process. A hundred years ago those costs were so high
that it only made sense to use security-style markets for a very limited range
of goods --- capital, in the forms of equity and bonds, and very raw factors of
production, like undifferentiated farm products and metals. As the transaction
costs of market allocation have fallen, so have the informational costs,
especially those arising from asymmetric information. This has expanded the
range of goods which can be securitized, and the range of securities which can
be offered. Crafting new instruments with different properties, especially
those relating to risk and the timing of returns, in and of itself reduces the
costs that arise from trying to force all means of raising capital for a firm
(say) into the form of selling equity, when other structures might make more
sense. The proliferation of instruments thus eases the task of making supply
and demand meet by requiring fewer trade-offs, and this is true whether the
supply and demand are those of capital for mortgages or electrical power. In
Scholes's vision, the goal of finance --- the justification for the stochastic
integrals and the derivative instruments --- is to simplify
decision-making for non-financiers. (One may believe this yet hold
reservations about the success of the undertaking.)

Scholes's theoretical contributions have received many honors, outstanding
among them, the 1997 Nobel Prize, shared with Merton. (Black had died the year
before, and the prize is not awarded posthumously.) Looking to the future, he
says that the most promising direction for finance is confronting
non-stationarity. Too much current work assumes stationarity, ergodicity, or
very weak non-stationarities like mean-reversion. The importance to risk
management of properly modeling large shocks is not likely to be lost on a man
whose was a partner in the Long-Term Capital Management fund, famously and
abruptly undone by just such shocks. But the broader intellectual point goes
beyond more or less ad hoc adjustments to deal with occasional shocks and
extreme values. Economies are not stationary even to first order, and
developing genuinely evolutionary models is essential to actually understanding
what markets do. What form non-stationary finance will take, no one can yet
say; that it will retain the contributions of Myron Scholes is certain.